Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.89942 | −1.09663 | −0.548315 | − | 0.836272i | \(-0.684730\pi\) | ||||
−0.548315 | + | 0.836272i | \(0.684730\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.311705 | 0.139399 | 0.0696993 | − | 0.997568i | \(-0.477796\pi\) | ||||
0.0696993 | + | 0.997568i | \(0.477796\pi\) | |||||||
\(6\) | −1.89942 | −0.775434 | ||||||||
\(7\) | 2.23532 | 0.844873 | 0.422437 | − | 0.906392i | \(-0.361175\pi\) | ||||
0.422437 | + | 0.906392i | \(0.361175\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.607790 | 0.202597 | ||||||||
\(10\) | 0.311705 | 0.0985697 | ||||||||
\(11\) | 4.25242 | 1.28215 | 0.641077 | − | 0.767477i | \(-0.278488\pi\) | ||||
0.641077 | + | 0.767477i | \(0.278488\pi\) | |||||||
\(12\) | −1.89942 | −0.548315 | ||||||||
\(13\) | 2.41091 | 0.668665 | 0.334332 | − | 0.942455i | \(-0.391489\pi\) | ||||
0.334332 | + | 0.942455i | \(0.391489\pi\) | |||||||
\(14\) | 2.23532 | 0.597416 | ||||||||
\(15\) | −0.592058 | −0.152869 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.75619 | 1.63862 | 0.819308 | − | 0.573353i | \(-0.194358\pi\) | ||||
0.819308 | + | 0.573353i | \(0.194358\pi\) | |||||||
\(18\) | 0.607790 | 0.143257 | ||||||||
\(19\) | −6.91293 | −1.58594 | −0.792968 | − | 0.609264i | \(-0.791465\pi\) | ||||
−0.792968 | + | 0.609264i | \(0.791465\pi\) | |||||||
\(20\) | 0.311705 | 0.0696993 | ||||||||
\(21\) | −4.24582 | −0.926513 | ||||||||
\(22\) | 4.25242 | 0.906619 | ||||||||
\(23\) | 5.68562 | 1.18553 | 0.592767 | − | 0.805374i | \(-0.298036\pi\) | ||||
0.592767 | + | 0.805374i | \(0.298036\pi\) | |||||||
\(24\) | −1.89942 | −0.387717 | ||||||||
\(25\) | −4.90284 | −0.980568 | ||||||||
\(26\) | 2.41091 | 0.472817 | ||||||||
\(27\) | 4.54381 | 0.874456 | ||||||||
\(28\) | 2.23532 | 0.422437 | ||||||||
\(29\) | 6.13276 | 1.13883 | 0.569413 | − | 0.822052i | \(-0.307171\pi\) | ||||
0.569413 | + | 0.822052i | \(0.307171\pi\) | |||||||
\(30\) | −0.592058 | −0.108094 | ||||||||
\(31\) | −3.55427 | −0.638366 | −0.319183 | − | 0.947693i | \(-0.603408\pi\) | ||||
−0.319183 | + | 0.947693i | \(0.603408\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −8.07713 | −1.40605 | ||||||||
\(34\) | 6.75619 | 1.15868 | ||||||||
\(35\) | 0.696762 | 0.117774 | ||||||||
\(36\) | 0.607790 | 0.101298 | ||||||||
\(37\) | −4.53006 | −0.744737 | −0.372369 | − | 0.928085i | \(-0.621454\pi\) | ||||
−0.372369 | + | 0.928085i | \(0.621454\pi\) | |||||||
\(38\) | −6.91293 | −1.12143 | ||||||||
\(39\) | −4.57932 | −0.733278 | ||||||||
\(40\) | 0.311705 | 0.0492849 | ||||||||
\(41\) | 2.55236 | 0.398611 | 0.199306 | − | 0.979937i | \(-0.436131\pi\) | ||||
0.199306 | + | 0.979937i | \(0.436131\pi\) | |||||||
\(42\) | −4.24582 | −0.655144 | ||||||||
\(43\) | 3.90707 | 0.595822 | 0.297911 | − | 0.954594i | \(-0.403710\pi\) | ||||
0.297911 | + | 0.954594i | \(0.403710\pi\) | |||||||
\(44\) | 4.25242 | 0.641077 | ||||||||
\(45\) | 0.189451 | 0.0282417 | ||||||||
\(46\) | 5.68562 | 0.838299 | ||||||||
\(47\) | −1.69908 | −0.247837 | −0.123918 | − | 0.992292i | \(-0.539546\pi\) | ||||
−0.123918 | + | 0.992292i | \(0.539546\pi\) | |||||||
\(48\) | −1.89942 | −0.274157 | ||||||||
\(49\) | −2.00332 | −0.286189 | ||||||||
\(50\) | −4.90284 | −0.693366 | ||||||||
\(51\) | −12.8328 | −1.79696 | ||||||||
\(52\) | 2.41091 | 0.334332 | ||||||||
\(53\) | 2.94978 | 0.405184 | 0.202592 | − | 0.979263i | \(-0.435063\pi\) | ||||
0.202592 | + | 0.979263i | \(0.435063\pi\) | |||||||
\(54\) | 4.54381 | 0.618334 | ||||||||
\(55\) | 1.32550 | 0.178730 | ||||||||
\(56\) | 2.23532 | 0.298708 | ||||||||
\(57\) | 13.1305 | 1.73918 | ||||||||
\(58\) | 6.13276 | 0.805271 | ||||||||
\(59\) | 2.92742 | 0.381118 | 0.190559 | − | 0.981676i | \(-0.438970\pi\) | ||||
0.190559 | + | 0.981676i | \(0.438970\pi\) | |||||||
\(60\) | −0.592058 | −0.0764343 | ||||||||
\(61\) | −7.23183 | −0.925941 | −0.462970 | − | 0.886374i | \(-0.653216\pi\) | ||||
−0.462970 | + | 0.886374i | \(0.653216\pi\) | |||||||
\(62\) | −3.55427 | −0.451393 | ||||||||
\(63\) | 1.35861 | 0.171168 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.751491 | 0.0932110 | ||||||||
\(66\) | −8.07713 | −0.994225 | ||||||||
\(67\) | −5.67176 | −0.692915 | −0.346458 | − | 0.938066i | \(-0.612616\pi\) | ||||
−0.346458 | + | 0.938066i | \(0.612616\pi\) | |||||||
\(68\) | 6.75619 | 0.819308 | ||||||||
\(69\) | −10.7994 | −1.30009 | ||||||||
\(70\) | 0.696762 | 0.0832789 | ||||||||
\(71\) | −11.3055 | −1.34172 | −0.670858 | − | 0.741586i | \(-0.734074\pi\) | ||||
−0.670858 | + | 0.741586i | \(0.734074\pi\) | |||||||
\(72\) | 0.607790 | 0.0716287 | ||||||||
\(73\) | 13.3499 | 1.56249 | 0.781244 | − | 0.624226i | \(-0.214586\pi\) | ||||
0.781244 | + | 0.624226i | \(0.214586\pi\) | |||||||
\(74\) | −4.53006 | −0.526609 | ||||||||
\(75\) | 9.31254 | 1.07532 | ||||||||
\(76\) | −6.91293 | −0.792968 | ||||||||
\(77\) | 9.50554 | 1.08326 | ||||||||
\(78\) | −4.57932 | −0.518506 | ||||||||
\(79\) | −2.07583 | −0.233550 | −0.116775 | − | 0.993158i | \(-0.537256\pi\) | ||||
−0.116775 | + | 0.993158i | \(0.537256\pi\) | |||||||
\(80\) | 0.311705 | 0.0348497 | ||||||||
\(81\) | −10.4540 | −1.16155 | ||||||||
\(82\) | 2.55236 | 0.281861 | ||||||||
\(83\) | −1.96803 | −0.216019 | −0.108010 | − | 0.994150i | \(-0.534448\pi\) | ||||
−0.108010 | + | 0.994150i | \(0.534448\pi\) | |||||||
\(84\) | −4.24582 | −0.463257 | ||||||||
\(85\) | 2.10594 | 0.228421 | ||||||||
\(86\) | 3.90707 | 0.421310 | ||||||||
\(87\) | −11.6487 | −1.24887 | ||||||||
\(88\) | 4.25242 | 0.453310 | ||||||||
\(89\) | 10.8323 | 1.14822 | 0.574109 | − | 0.818779i | \(-0.305348\pi\) | ||||
0.574109 | + | 0.818779i | \(0.305348\pi\) | |||||||
\(90\) | 0.189451 | 0.0199699 | ||||||||
\(91\) | 5.38916 | 0.564937 | ||||||||
\(92\) | 5.68562 | 0.592767 | ||||||||
\(93\) | 6.75105 | 0.700051 | ||||||||
\(94\) | −1.69908 | −0.175247 | ||||||||
\(95\) | −2.15479 | −0.221077 | ||||||||
\(96\) | −1.89942 | −0.193859 | ||||||||
\(97\) | −8.30633 | −0.843380 | −0.421690 | − | 0.906740i | \(-0.638563\pi\) | ||||
−0.421690 | + | 0.906740i | \(0.638563\pi\) | |||||||
\(98\) | −2.00332 | −0.202366 | ||||||||
\(99\) | 2.58458 | 0.259760 | ||||||||
\(100\) | −4.90284 | −0.490284 | ||||||||
\(101\) | 2.30019 | 0.228877 | 0.114439 | − | 0.993430i | \(-0.463493\pi\) | ||||
0.114439 | + | 0.993430i | \(0.463493\pi\) | |||||||
\(102\) | −12.8328 | −1.27064 | ||||||||
\(103\) | 13.9502 | 1.37456 | 0.687279 | − | 0.726394i | \(-0.258805\pi\) | ||||
0.687279 | + | 0.726394i | \(0.258805\pi\) | |||||||
\(104\) | 2.41091 | 0.236409 | ||||||||
\(105\) | −1.32344 | −0.129155 | ||||||||
\(106\) | 2.94978 | 0.286508 | ||||||||
\(107\) | 12.5091 | 1.20930 | 0.604651 | − | 0.796490i | \(-0.293313\pi\) | ||||
0.604651 | + | 0.796490i | \(0.293313\pi\) | |||||||
\(108\) | 4.54381 | 0.437228 | ||||||||
\(109\) | −12.7578 | −1.22198 | −0.610989 | − | 0.791639i | \(-0.709228\pi\) | ||||
−0.610989 | + | 0.791639i | \(0.709228\pi\) | |||||||
\(110\) | 1.32550 | 0.126381 | ||||||||
\(111\) | 8.60448 | 0.816701 | ||||||||
\(112\) | 2.23532 | 0.211218 | ||||||||
\(113\) | 7.72790 | 0.726980 | 0.363490 | − | 0.931598i | \(-0.381585\pi\) | ||||
0.363490 | + | 0.931598i | \(0.381585\pi\) | |||||||
\(114\) | 13.1305 | 1.22979 | ||||||||
\(115\) | 1.77224 | 0.165262 | ||||||||
\(116\) | 6.13276 | 0.569413 | ||||||||
\(117\) | 1.46532 | 0.135469 | ||||||||
\(118\) | 2.92742 | 0.269491 | ||||||||
\(119\) | 15.1023 | 1.38442 | ||||||||
\(120\) | −0.592058 | −0.0540472 | ||||||||
\(121\) | 7.08308 | 0.643917 | ||||||||
\(122\) | −7.23183 | −0.654739 | ||||||||
\(123\) | −4.84799 | −0.437129 | ||||||||
\(124\) | −3.55427 | −0.319183 | ||||||||
\(125\) | −3.08676 | −0.276088 | ||||||||
\(126\) | 1.35861 | 0.121034 | ||||||||
\(127\) | −1.81770 | −0.161295 | −0.0806474 | − | 0.996743i | \(-0.525699\pi\) | ||||
−0.0806474 | + | 0.996743i | \(0.525699\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.42115 | −0.653396 | ||||||||
\(130\) | 0.751491 | 0.0659101 | ||||||||
\(131\) | 20.7507 | 1.81300 | 0.906499 | − | 0.422209i | \(-0.138745\pi\) | ||||
0.906499 | + | 0.422209i | \(0.138745\pi\) | |||||||
\(132\) | −8.07713 | −0.703024 | ||||||||
\(133\) | −15.4526 | −1.33991 | ||||||||
\(134\) | −5.67176 | −0.489965 | ||||||||
\(135\) | 1.41633 | 0.121898 | ||||||||
\(136\) | 6.75619 | 0.579338 | ||||||||
\(137\) | −9.23510 | −0.789008 | −0.394504 | − | 0.918894i | \(-0.629084\pi\) | ||||
−0.394504 | + | 0.918894i | \(0.629084\pi\) | |||||||
\(138\) | −10.7994 | −0.919303 | ||||||||
\(139\) | −8.85808 | −0.751333 | −0.375666 | − | 0.926755i | \(-0.622586\pi\) | ||||
−0.375666 | + | 0.926755i | \(0.622586\pi\) | |||||||
\(140\) | 0.696762 | 0.0588871 | ||||||||
\(141\) | 3.22727 | 0.271785 | ||||||||
\(142\) | −11.3055 | −0.948736 | ||||||||
\(143\) | 10.2522 | 0.857331 | ||||||||
\(144\) | 0.607790 | 0.0506491 | ||||||||
\(145\) | 1.91161 | 0.158751 | ||||||||
\(146\) | 13.3499 | 1.10485 | ||||||||
\(147\) | 3.80515 | 0.313843 | ||||||||
\(148\) | −4.53006 | −0.372369 | ||||||||
\(149\) | 7.93318 | 0.649911 | 0.324956 | − | 0.945729i | \(-0.394651\pi\) | ||||
0.324956 | + | 0.945729i | \(0.394651\pi\) | |||||||
\(150\) | 9.31254 | 0.760366 | ||||||||
\(151\) | −16.7113 | −1.35994 | −0.679972 | − | 0.733238i | \(-0.738008\pi\) | ||||
−0.679972 | + | 0.733238i | \(0.738008\pi\) | |||||||
\(152\) | −6.91293 | −0.560713 | ||||||||
\(153\) | 4.10634 | 0.331978 | ||||||||
\(154\) | 9.50554 | 0.765978 | ||||||||
\(155\) | −1.10788 | −0.0889874 | ||||||||
\(156\) | −4.57932 | −0.366639 | ||||||||
\(157\) | 20.4744 | 1.63404 | 0.817019 | − | 0.576611i | \(-0.195625\pi\) | ||||
0.817019 | + | 0.576611i | \(0.195625\pi\) | |||||||
\(158\) | −2.07583 | −0.165145 | ||||||||
\(159\) | −5.60287 | −0.444337 | ||||||||
\(160\) | 0.311705 | 0.0246424 | ||||||||
\(161\) | 12.7092 | 1.00163 | ||||||||
\(162\) | −10.4540 | −0.821341 | ||||||||
\(163\) | 9.00051 | 0.704974 | 0.352487 | − | 0.935817i | \(-0.385336\pi\) | ||||
0.352487 | + | 0.935817i | \(0.385336\pi\) | |||||||
\(164\) | 2.55236 | 0.199306 | ||||||||
\(165\) | −2.51768 | −0.196001 | ||||||||
\(166\) | −1.96803 | −0.152749 | ||||||||
\(167\) | −8.99976 | −0.696423 | −0.348211 | − | 0.937416i | \(-0.613211\pi\) | ||||
−0.348211 | + | 0.937416i | \(0.613211\pi\) | |||||||
\(168\) | −4.24582 | −0.327572 | ||||||||
\(169\) | −7.18754 | −0.552887 | ||||||||
\(170\) | 2.10594 | 0.161518 | ||||||||
\(171\) | −4.20161 | −0.321305 | ||||||||
\(172\) | 3.90707 | 0.297911 | ||||||||
\(173\) | 22.3103 | 1.69622 | 0.848111 | − | 0.529818i | \(-0.177740\pi\) | ||||
0.848111 | + | 0.529818i | \(0.177740\pi\) | |||||||
\(174\) | −11.6487 | −0.883084 | ||||||||
\(175\) | −10.9594 | −0.828456 | ||||||||
\(176\) | 4.25242 | 0.320538 | ||||||||
\(177\) | −5.56039 | −0.417945 | ||||||||
\(178\) | 10.8323 | 0.811913 | ||||||||
\(179\) | 2.24497 | 0.167797 | 0.0838983 | − | 0.996474i | \(-0.473263\pi\) | ||||
0.0838983 | + | 0.996474i | \(0.473263\pi\) | |||||||
\(180\) | 0.189451 | 0.0141208 | ||||||||
\(181\) | 12.7432 | 0.947194 | 0.473597 | − | 0.880742i | \(-0.342955\pi\) | ||||
0.473597 | + | 0.880742i | \(0.342955\pi\) | |||||||
\(182\) | 5.38916 | 0.399471 | ||||||||
\(183\) | 13.7363 | 1.01541 | ||||||||
\(184\) | 5.68562 | 0.419149 | ||||||||
\(185\) | −1.41204 | −0.103815 | ||||||||
\(186\) | 6.75105 | 0.495011 | ||||||||
\(187\) | 28.7302 | 2.10096 | ||||||||
\(188\) | −1.69908 | −0.123918 | ||||||||
\(189\) | 10.1569 | 0.738805 | ||||||||
\(190\) | −2.15479 | −0.156325 | ||||||||
\(191\) | 4.09996 | 0.296662 | 0.148331 | − | 0.988938i | \(-0.452610\pi\) | ||||
0.148331 | + | 0.988938i | \(0.452610\pi\) | |||||||
\(192\) | −1.89942 | −0.137079 | ||||||||
\(193\) | 21.8203 | 1.57066 | 0.785331 | − | 0.619077i | \(-0.212493\pi\) | ||||
0.785331 | + | 0.619077i | \(0.212493\pi\) | |||||||
\(194\) | −8.30633 | −0.596359 | ||||||||
\(195\) | −1.42740 | −0.102218 | ||||||||
\(196\) | −2.00332 | −0.143094 | ||||||||
\(197\) | −8.72843 | −0.621875 | −0.310938 | − | 0.950430i | \(-0.600643\pi\) | ||||
−0.310938 | + | 0.950430i | \(0.600643\pi\) | |||||||
\(198\) | 2.58458 | 0.183678 | ||||||||
\(199\) | −13.5977 | −0.963917 | −0.481959 | − | 0.876194i | \(-0.660074\pi\) | ||||
−0.481959 | + | 0.876194i | \(0.660074\pi\) | |||||||
\(200\) | −4.90284 | −0.346683 | ||||||||
\(201\) | 10.7730 | 0.759872 | ||||||||
\(202\) | 2.30019 | 0.161841 | ||||||||
\(203\) | 13.7087 | 0.962163 | ||||||||
\(204\) | −12.8328 | −0.898478 | ||||||||
\(205\) | 0.795582 | 0.0555659 | ||||||||
\(206\) | 13.9502 | 0.971959 | ||||||||
\(207\) | 3.45566 | 0.240185 | ||||||||
\(208\) | 2.41091 | 0.167166 | ||||||||
\(209\) | −29.3967 | −2.03341 | ||||||||
\(210\) | −1.32344 | −0.0913262 | ||||||||
\(211\) | −18.8210 | −1.29569 | −0.647847 | − | 0.761771i | \(-0.724330\pi\) | ||||
−0.647847 | + | 0.761771i | \(0.724330\pi\) | |||||||
\(212\) | 2.94978 | 0.202592 | ||||||||
\(213\) | 21.4739 | 1.47137 | ||||||||
\(214\) | 12.5091 | 0.855106 | ||||||||
\(215\) | 1.21785 | 0.0830568 | ||||||||
\(216\) | 4.54381 | 0.309167 | ||||||||
\(217\) | −7.94495 | −0.539339 | ||||||||
\(218\) | −12.7578 | −0.864068 | ||||||||
\(219\) | −25.3570 | −1.71347 | ||||||||
\(220\) | 1.32550 | 0.0893652 | ||||||||
\(221\) | 16.2885 | 1.09569 | ||||||||
\(222\) | 8.60448 | 0.577495 | ||||||||
\(223\) | 13.0119 | 0.871338 | 0.435669 | − | 0.900107i | \(-0.356512\pi\) | ||||
0.435669 | + | 0.900107i | \(0.356512\pi\) | |||||||
\(224\) | 2.23532 | 0.149354 | ||||||||
\(225\) | −2.97990 | −0.198660 | ||||||||
\(226\) | 7.72790 | 0.514053 | ||||||||
\(227\) | 25.5480 | 1.69568 | 0.847840 | − | 0.530252i | \(-0.177903\pi\) | ||||
0.847840 | + | 0.530252i | \(0.177903\pi\) | |||||||
\(228\) | 13.1305 | 0.869592 | ||||||||
\(229\) | 10.1907 | 0.673420 | 0.336710 | − | 0.941608i | \(-0.390686\pi\) | ||||
0.336710 | + | 0.941608i | \(0.390686\pi\) | |||||||
\(230\) | 1.77224 | 0.116858 | ||||||||
\(231\) | −18.0550 | −1.18793 | ||||||||
\(232\) | 6.13276 | 0.402636 | ||||||||
\(233\) | −25.3591 | −1.66133 | −0.830666 | − | 0.556771i | \(-0.812040\pi\) | ||||
−0.830666 | + | 0.556771i | \(0.812040\pi\) | |||||||
\(234\) | 1.46532 | 0.0957912 | ||||||||
\(235\) | −0.529612 | −0.0345481 | ||||||||
\(236\) | 2.92742 | 0.190559 | ||||||||
\(237\) | 3.94288 | 0.256117 | ||||||||
\(238\) | 15.1023 | 0.978935 | ||||||||
\(239\) | 18.9875 | 1.22820 | 0.614099 | − | 0.789229i | \(-0.289519\pi\) | ||||
0.614099 | + | 0.789229i | \(0.289519\pi\) | |||||||
\(240\) | −0.592058 | −0.0382172 | ||||||||
\(241\) | 19.6887 | 1.26826 | 0.634130 | − | 0.773226i | \(-0.281358\pi\) | ||||
0.634130 | + | 0.773226i | \(0.281358\pi\) | |||||||
\(242\) | 7.08308 | 0.455318 | ||||||||
\(243\) | 6.22502 | 0.399335 | ||||||||
\(244\) | −7.23183 | −0.462970 | ||||||||
\(245\) | −0.624445 | −0.0398944 | ||||||||
\(246\) | −4.84799 | −0.309097 | ||||||||
\(247\) | −16.6664 | −1.06046 | ||||||||
\(248\) | −3.55427 | −0.225697 | ||||||||
\(249\) | 3.73811 | 0.236893 | ||||||||
\(250\) | −3.08676 | −0.195224 | ||||||||
\(251\) | −0.426326 | −0.0269095 | −0.0134547 | − | 0.999909i | \(-0.504283\pi\) | ||||
−0.0134547 | + | 0.999909i | \(0.504283\pi\) | |||||||
\(252\) | 1.35861 | 0.0855842 | ||||||||
\(253\) | 24.1777 | 1.52004 | ||||||||
\(254\) | −1.81770 | −0.114053 | ||||||||
\(255\) | −4.00005 | −0.250493 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.0153 | 1.62279 | 0.811394 | − | 0.584500i | \(-0.198709\pi\) | ||||
0.811394 | + | 0.584500i | \(0.198709\pi\) | |||||||
\(258\) | −7.42115 | −0.462021 | ||||||||
\(259\) | −10.1262 | −0.629209 | ||||||||
\(260\) | 0.751491 | 0.0466055 | ||||||||
\(261\) | 3.72743 | 0.230722 | ||||||||
\(262\) | 20.7507 | 1.28198 | ||||||||
\(263\) | −13.9916 | −0.862761 | −0.431380 | − | 0.902170i | \(-0.641973\pi\) | ||||
−0.431380 | + | 0.902170i | \(0.641973\pi\) | |||||||
\(264\) | −8.07713 | −0.497113 | ||||||||
\(265\) | 0.919462 | 0.0564821 | ||||||||
\(266\) | −15.4526 | −0.947463 | ||||||||
\(267\) | −20.5750 | −1.25917 | ||||||||
\(268\) | −5.67176 | −0.346458 | ||||||||
\(269\) | 12.6808 | 0.773163 | 0.386581 | − | 0.922255i | \(-0.373656\pi\) | ||||
0.386581 | + | 0.922255i | \(0.373656\pi\) | |||||||
\(270\) | 1.41633 | 0.0861949 | ||||||||
\(271\) | 0.812497 | 0.0493557 | 0.0246778 | − | 0.999695i | \(-0.492144\pi\) | ||||
0.0246778 | + | 0.999695i | \(0.492144\pi\) | |||||||
\(272\) | 6.75619 | 0.409654 | ||||||||
\(273\) | −10.2363 | −0.619527 | ||||||||
\(274\) | −9.23510 | −0.557913 | ||||||||
\(275\) | −20.8489 | −1.25724 | ||||||||
\(276\) | −10.7994 | −0.650046 | ||||||||
\(277\) | −2.28077 | −0.137038 | −0.0685191 | − | 0.997650i | \(-0.521827\pi\) | ||||
−0.0685191 | + | 0.997650i | \(0.521827\pi\) | |||||||
\(278\) | −8.85808 | −0.531272 | ||||||||
\(279\) | −2.16025 | −0.129331 | ||||||||
\(280\) | 0.696762 | 0.0416395 | ||||||||
\(281\) | −21.2897 | −1.27004 | −0.635018 | − | 0.772497i | \(-0.719007\pi\) | ||||
−0.635018 | + | 0.772497i | \(0.719007\pi\) | |||||||
\(282\) | 3.22727 | 0.192181 | ||||||||
\(283\) | −23.5640 | −1.40074 | −0.700368 | − | 0.713782i | \(-0.746981\pi\) | ||||
−0.700368 | + | 0.713782i | \(0.746981\pi\) | |||||||
\(284\) | −11.3055 | −0.670858 | ||||||||
\(285\) | 4.09286 | 0.242440 | ||||||||
\(286\) | 10.2522 | 0.606224 | ||||||||
\(287\) | 5.70535 | 0.336776 | ||||||||
\(288\) | 0.607790 | 0.0358144 | ||||||||
\(289\) | 28.6461 | 1.68506 | ||||||||
\(290\) | 1.91161 | 0.112254 | ||||||||
\(291\) | 15.7772 | 0.924875 | ||||||||
\(292\) | 13.3499 | 0.781244 | ||||||||
\(293\) | 6.89229 | 0.402652 | 0.201326 | − | 0.979524i | \(-0.435475\pi\) | ||||
0.201326 | + | 0.979524i | \(0.435475\pi\) | |||||||
\(294\) | 3.80515 | 0.221921 | ||||||||
\(295\) | 0.912491 | 0.0531273 | ||||||||
\(296\) | −4.53006 | −0.263304 | ||||||||
\(297\) | 19.3222 | 1.12119 | ||||||||
\(298\) | 7.93318 | 0.459557 | ||||||||
\(299\) | 13.7075 | 0.792725 | ||||||||
\(300\) | 9.31254 | 0.537660 | ||||||||
\(301\) | 8.73356 | 0.503394 | ||||||||
\(302\) | −16.7113 | −0.961625 | ||||||||
\(303\) | −4.36902 | −0.250994 | ||||||||
\(304\) | −6.91293 | −0.396484 | ||||||||
\(305\) | −2.25420 | −0.129075 | ||||||||
\(306\) | 4.10634 | 0.234744 | ||||||||
\(307\) | −18.3766 | −1.04881 | −0.524404 | − | 0.851470i | \(-0.675712\pi\) | ||||
−0.524404 | + | 0.851470i | \(0.675712\pi\) | |||||||
\(308\) | 9.50554 | 0.541629 | ||||||||
\(309\) | −26.4973 | −1.50738 | ||||||||
\(310\) | −1.10788 | −0.0629236 | ||||||||
\(311\) | −31.6409 | −1.79419 | −0.897095 | − | 0.441837i | \(-0.854327\pi\) | ||||
−0.897095 | + | 0.441837i | \(0.854327\pi\) | |||||||
\(312\) | −4.57932 | −0.259253 | ||||||||
\(313\) | −3.70011 | −0.209142 | −0.104571 | − | 0.994517i | \(-0.533347\pi\) | ||||
−0.104571 | + | 0.994517i | \(0.533347\pi\) | |||||||
\(314\) | 20.4744 | 1.15544 | ||||||||
\(315\) | 0.423485 | 0.0238606 | ||||||||
\(316\) | −2.07583 | −0.116775 | ||||||||
\(317\) | −33.4390 | −1.87812 | −0.939061 | − | 0.343749i | \(-0.888303\pi\) | ||||
−0.939061 | + | 0.343749i | \(0.888303\pi\) | |||||||
\(318\) | −5.60287 | −0.314194 | ||||||||
\(319\) | 26.0791 | 1.46015 | ||||||||
\(320\) | 0.311705 | 0.0174248 | ||||||||
\(321\) | −23.7600 | −1.32616 | ||||||||
\(322\) | 12.7092 | 0.708256 | ||||||||
\(323\) | −46.7051 | −2.59874 | ||||||||
\(324\) | −10.4540 | −0.580776 | ||||||||
\(325\) | −11.8203 | −0.655671 | ||||||||
\(326\) | 9.00051 | 0.498492 | ||||||||
\(327\) | 24.2324 | 1.34006 | ||||||||
\(328\) | 2.55236 | 0.140930 | ||||||||
\(329\) | −3.79800 | −0.209391 | ||||||||
\(330\) | −2.51768 | −0.138594 | ||||||||
\(331\) | 25.9855 | 1.42829 | 0.714146 | − | 0.699996i | \(-0.246815\pi\) | ||||
0.714146 | + | 0.699996i | \(0.246815\pi\) | |||||||
\(332\) | −1.96803 | −0.108010 | ||||||||
\(333\) | −2.75332 | −0.150881 | ||||||||
\(334\) | −8.99976 | −0.492445 | ||||||||
\(335\) | −1.76791 | −0.0965915 | ||||||||
\(336\) | −4.24582 | −0.231628 | ||||||||
\(337\) | 25.7759 | 1.40410 | 0.702051 | − | 0.712127i | \(-0.252268\pi\) | ||||
0.702051 | + | 0.712127i | \(0.252268\pi\) | |||||||
\(338\) | −7.18754 | −0.390950 | ||||||||
\(339\) | −14.6785 | −0.797228 | ||||||||
\(340\) | 2.10594 | 0.114210 | ||||||||
\(341\) | −15.1143 | −0.818483 | ||||||||
\(342\) | −4.20161 | −0.227197 | ||||||||
\(343\) | −20.1254 | −1.08667 | ||||||||
\(344\) | 3.90707 | 0.210655 | ||||||||
\(345\) | −3.36622 | −0.181231 | ||||||||
\(346\) | 22.3103 | 1.19941 | ||||||||
\(347\) | −4.89860 | −0.262971 | −0.131485 | − | 0.991318i | \(-0.541975\pi\) | ||||
−0.131485 | + | 0.991318i | \(0.541975\pi\) | |||||||
\(348\) | −11.6487 | −0.624435 | ||||||||
\(349\) | 9.62083 | 0.514991 | 0.257496 | − | 0.966279i | \(-0.417103\pi\) | ||||
0.257496 | + | 0.966279i | \(0.417103\pi\) | |||||||
\(350\) | −10.9594 | −0.585807 | ||||||||
\(351\) | 10.9547 | 0.584718 | ||||||||
\(352\) | 4.25242 | 0.226655 | ||||||||
\(353\) | 6.69700 | 0.356446 | 0.178223 | − | 0.983990i | \(-0.442965\pi\) | ||||
0.178223 | + | 0.983990i | \(0.442965\pi\) | |||||||
\(354\) | −5.56039 | −0.295532 | ||||||||
\(355\) | −3.52398 | −0.187033 | ||||||||
\(356\) | 10.8323 | 0.574109 | ||||||||
\(357\) | −28.6855 | −1.51820 | ||||||||
\(358\) | 2.24497 | 0.118650 | ||||||||
\(359\) | 22.8379 | 1.20534 | 0.602669 | − | 0.797991i | \(-0.294104\pi\) | ||||
0.602669 | + | 0.797991i | \(0.294104\pi\) | |||||||
\(360\) | 0.189451 | 0.00998494 | ||||||||
\(361\) | 28.7886 | 1.51519 | ||||||||
\(362\) | 12.7432 | 0.669767 | ||||||||
\(363\) | −13.4537 | −0.706138 | ||||||||
\(364\) | 5.38916 | 0.282469 | ||||||||
\(365\) | 4.16123 | 0.217809 | ||||||||
\(366\) | 13.7363 | 0.718006 | ||||||||
\(367\) | −3.88121 | −0.202597 | −0.101299 | − | 0.994856i | \(-0.532300\pi\) | ||||
−0.101299 | + | 0.994856i | \(0.532300\pi\) | |||||||
\(368\) | 5.68562 | 0.296383 | ||||||||
\(369\) | 1.55130 | 0.0807573 | ||||||||
\(370\) | −1.41204 | −0.0734085 | ||||||||
\(371\) | 6.59373 | 0.342329 | ||||||||
\(372\) | 6.75105 | 0.350026 | ||||||||
\(373\) | 29.4760 | 1.52621 | 0.763104 | − | 0.646276i | \(-0.223675\pi\) | ||||
0.763104 | + | 0.646276i | \(0.223675\pi\) | |||||||
\(374\) | 28.7302 | 1.48560 | ||||||||
\(375\) | 5.86305 | 0.302767 | ||||||||
\(376\) | −1.69908 | −0.0876235 | ||||||||
\(377\) | 14.7855 | 0.761492 | ||||||||
\(378\) | 10.1569 | 0.522414 | ||||||||
\(379\) | −34.7667 | −1.78585 | −0.892924 | − | 0.450208i | \(-0.851350\pi\) | ||||
−0.892924 | + | 0.450208i | \(0.851350\pi\) | |||||||
\(380\) | −2.15479 | −0.110539 | ||||||||
\(381\) | 3.45257 | 0.176881 | ||||||||
\(382\) | 4.09996 | 0.209772 | ||||||||
\(383\) | −24.4903 | −1.25139 | −0.625697 | − | 0.780066i | \(-0.715185\pi\) | ||||
−0.625697 | + | 0.780066i | \(0.715185\pi\) | |||||||
\(384\) | −1.89942 | −0.0969293 | ||||||||
\(385\) | 2.96292 | 0.151005 | ||||||||
\(386\) | 21.8203 | 1.11063 | ||||||||
\(387\) | 2.37468 | 0.120712 | ||||||||
\(388\) | −8.30633 | −0.421690 | ||||||||
\(389\) | −13.4112 | −0.679974 | −0.339987 | − | 0.940430i | \(-0.610423\pi\) | ||||
−0.339987 | + | 0.940430i | \(0.610423\pi\) | |||||||
\(390\) | −1.42740 | −0.0722790 | ||||||||
\(391\) | 38.4131 | 1.94263 | ||||||||
\(392\) | −2.00332 | −0.101183 | ||||||||
\(393\) | −39.4143 | −1.98819 | ||||||||
\(394\) | −8.72843 | −0.439732 | ||||||||
\(395\) | −0.647048 | −0.0325565 | ||||||||
\(396\) | 2.58458 | 0.129880 | ||||||||
\(397\) | 10.1924 | 0.511542 | 0.255771 | − | 0.966737i | \(-0.417671\pi\) | ||||
0.255771 | + | 0.966737i | \(0.417671\pi\) | |||||||
\(398\) | −13.5977 | −0.681592 | ||||||||
\(399\) | 29.3510 | 1.46939 | ||||||||
\(400\) | −4.90284 | −0.245142 | ||||||||
\(401\) | −13.8909 | −0.693677 | −0.346838 | − | 0.937925i | \(-0.612745\pi\) | ||||
−0.346838 | + | 0.937925i | \(0.612745\pi\) | |||||||
\(402\) | 10.7730 | 0.537310 | ||||||||
\(403\) | −8.56901 | −0.426853 | ||||||||
\(404\) | 2.30019 | 0.114439 | ||||||||
\(405\) | −3.25855 | −0.161919 | ||||||||
\(406\) | 13.7087 | 0.680352 | ||||||||
\(407\) | −19.2637 | −0.954867 | ||||||||
\(408\) | −12.8328 | −0.635320 | ||||||||
\(409\) | −10.4113 | −0.514807 | −0.257403 | − | 0.966304i | \(-0.582867\pi\) | ||||
−0.257403 | + | 0.966304i | \(0.582867\pi\) | |||||||
\(410\) | 0.795582 | 0.0392910 | ||||||||
\(411\) | 17.5413 | 0.865250 | ||||||||
\(412\) | 13.9502 | 0.687279 | ||||||||
\(413\) | 6.54373 | 0.321996 | ||||||||
\(414\) | 3.45566 | 0.169836 | ||||||||
\(415\) | −0.613444 | −0.0301128 | ||||||||
\(416\) | 2.41091 | 0.118204 | ||||||||
\(417\) | 16.8252 | 0.823934 | ||||||||
\(418\) | −29.3967 | −1.43784 | ||||||||
\(419\) | −31.1890 | −1.52368 | −0.761841 | − | 0.647765i | \(-0.775704\pi\) | ||||
−0.761841 | + | 0.647765i | \(0.775704\pi\) | |||||||
\(420\) | −1.32344 | −0.0645773 | ||||||||
\(421\) | −13.4321 | −0.654639 | −0.327319 | − | 0.944914i | \(-0.606145\pi\) | ||||
−0.327319 | + | 0.944914i | \(0.606145\pi\) | |||||||
\(422\) | −18.8210 | −0.916194 | ||||||||
\(423\) | −1.03269 | −0.0502109 | ||||||||
\(424\) | 2.94978 | 0.143254 | ||||||||
\(425\) | −33.1245 | −1.60677 | ||||||||
\(426\) | 21.4739 | 1.04041 | ||||||||
\(427\) | −16.1655 | −0.782303 | ||||||||
\(428\) | 12.5091 | 0.604651 | ||||||||
\(429\) | −19.4732 | −0.940174 | ||||||||
\(430\) | 1.21785 | 0.0587300 | ||||||||
\(431\) | 25.7669 | 1.24115 | 0.620573 | − | 0.784149i | \(-0.286900\pi\) | ||||
0.620573 | + | 0.784149i | \(0.286900\pi\) | |||||||
\(432\) | 4.54381 | 0.218614 | ||||||||
\(433\) | −31.6498 | −1.52099 | −0.760495 | − | 0.649344i | \(-0.775044\pi\) | ||||
−0.760495 | + | 0.649344i | \(0.775044\pi\) | |||||||
\(434\) | −7.94495 | −0.381370 | ||||||||
\(435\) | −3.63095 | −0.174091 | ||||||||
\(436\) | −12.7578 | −0.610989 | ||||||||
\(437\) | −39.3043 | −1.88018 | ||||||||
\(438\) | −25.3570 | −1.21161 | ||||||||
\(439\) | −22.3643 | −1.06739 | −0.533694 | − | 0.845678i | \(-0.679197\pi\) | ||||
−0.533694 | + | 0.845678i | \(0.679197\pi\) | |||||||
\(440\) | 1.32550 | 0.0631907 | ||||||||
\(441\) | −1.21760 | −0.0579809 | ||||||||
\(442\) | 16.2885 | 0.774766 | ||||||||
\(443\) | 30.5556 | 1.45174 | 0.725871 | − | 0.687831i | \(-0.241437\pi\) | ||||
0.725871 | + | 0.687831i | \(0.241437\pi\) | |||||||
\(444\) | 8.60448 | 0.408350 | ||||||||
\(445\) | 3.37647 | 0.160060 | ||||||||
\(446\) | 13.0119 | 0.616129 | ||||||||
\(447\) | −15.0684 | −0.712712 | ||||||||
\(448\) | 2.23532 | 0.105609 | ||||||||
\(449\) | 24.7092 | 1.16610 | 0.583049 | − | 0.812437i | \(-0.301859\pi\) | ||||
0.583049 | + | 0.812437i | \(0.301859\pi\) | |||||||
\(450\) | −2.97990 | −0.140474 | ||||||||
\(451\) | 10.8537 | 0.511081 | ||||||||
\(452\) | 7.72790 | 0.363490 | ||||||||
\(453\) | 31.7417 | 1.49135 | ||||||||
\(454\) | 25.5480 | 1.19903 | ||||||||
\(455\) | 1.67983 | 0.0787515 | ||||||||
\(456\) | 13.1305 | 0.614894 | ||||||||
\(457\) | −37.6152 | −1.75957 | −0.879783 | − | 0.475376i | \(-0.842312\pi\) | ||||
−0.879783 | + | 0.475376i | \(0.842312\pi\) | |||||||
\(458\) | 10.1907 | 0.476180 | ||||||||
\(459\) | 30.6988 | 1.43290 | ||||||||
\(460\) | 1.77224 | 0.0826309 | ||||||||
\(461\) | 12.8721 | 0.599516 | 0.299758 | − | 0.954015i | \(-0.403094\pi\) | ||||
0.299758 | + | 0.954015i | \(0.403094\pi\) | |||||||
\(462\) | −18.0550 | −0.839995 | ||||||||
\(463\) | 32.6181 | 1.51589 | 0.757947 | − | 0.652317i | \(-0.226203\pi\) | ||||
0.757947 | + | 0.652317i | \(0.226203\pi\) | |||||||
\(464\) | 6.13276 | 0.284706 | ||||||||
\(465\) | 2.10433 | 0.0975862 | ||||||||
\(466\) | −25.3591 | −1.17474 | ||||||||
\(467\) | −4.90131 | −0.226805 | −0.113403 | − | 0.993549i | \(-0.536175\pi\) | ||||
−0.113403 | + | 0.993549i | \(0.536175\pi\) | |||||||
\(468\) | 1.46532 | 0.0677346 | ||||||||
\(469\) | −12.6782 | −0.585426 | ||||||||
\(470\) | −0.529612 | −0.0244292 | ||||||||
\(471\) | −38.8895 | −1.79193 | ||||||||
\(472\) | 2.92742 | 0.134745 | ||||||||
\(473\) | 16.6145 | 0.763935 | ||||||||
\(474\) | 3.94288 | 0.181102 | ||||||||
\(475\) | 33.8930 | 1.55512 | ||||||||
\(476\) | 15.1023 | 0.692212 | ||||||||
\(477\) | 1.79285 | 0.0820889 | ||||||||
\(478\) | 18.9875 | 0.868467 | ||||||||
\(479\) | −3.59924 | −0.164453 | −0.0822267 | − | 0.996614i | \(-0.526203\pi\) | ||||
−0.0822267 | + | 0.996614i | \(0.526203\pi\) | |||||||
\(480\) | −0.592058 | −0.0270236 | ||||||||
\(481\) | −10.9215 | −0.497980 | ||||||||
\(482\) | 19.6887 | 0.896796 | ||||||||
\(483\) | −24.1401 | −1.09841 | ||||||||
\(484\) | 7.08308 | 0.321958 | ||||||||
\(485\) | −2.58912 | −0.117566 | ||||||||
\(486\) | 6.22502 | 0.282373 | ||||||||
\(487\) | 0.985032 | 0.0446361 | 0.0223180 | − | 0.999751i | \(-0.492895\pi\) | ||||
0.0223180 | + | 0.999751i | \(0.492895\pi\) | |||||||
\(488\) | −7.23183 | −0.327370 | ||||||||
\(489\) | −17.0957 | −0.773095 | ||||||||
\(490\) | −0.624445 | −0.0282096 | ||||||||
\(491\) | −29.3140 | −1.32292 | −0.661461 | − | 0.749979i | \(-0.730063\pi\) | ||||
−0.661461 | + | 0.749979i | \(0.730063\pi\) | |||||||
\(492\) | −4.84799 | −0.218564 | ||||||||
\(493\) | 41.4341 | 1.86610 | ||||||||
\(494\) | −16.6664 | −0.749858 | ||||||||
\(495\) | 0.805625 | 0.0362102 | ||||||||
\(496\) | −3.55427 | −0.159592 | ||||||||
\(497\) | −25.2715 | −1.13358 | ||||||||
\(498\) | 3.73811 | 0.167509 | ||||||||
\(499\) | −6.20797 | −0.277907 | −0.138954 | − | 0.990299i | \(-0.544374\pi\) | ||||
−0.138954 | + | 0.990299i | \(0.544374\pi\) | |||||||
\(500\) | −3.08676 | −0.138044 | ||||||||
\(501\) | 17.0943 | 0.763718 | ||||||||
\(502\) | −0.426326 | −0.0190279 | ||||||||
\(503\) | −23.8116 | −1.06171 | −0.530853 | − | 0.847464i | \(-0.678128\pi\) | ||||
−0.530853 | + | 0.847464i | \(0.678128\pi\) | |||||||
\(504\) | 1.35861 | 0.0605172 | ||||||||
\(505\) | 0.716980 | 0.0319052 | ||||||||
\(506\) | 24.1777 | 1.07483 | ||||||||
\(507\) | 13.6521 | 0.606313 | ||||||||
\(508\) | −1.81770 | −0.0806474 | ||||||||
\(509\) | −19.1006 | −0.846620 | −0.423310 | − | 0.905985i | \(-0.639132\pi\) | ||||
−0.423310 | + | 0.905985i | \(0.639132\pi\) | |||||||
\(510\) | −4.00005 | −0.177125 | ||||||||
\(511\) | 29.8414 | 1.32010 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −31.4110 | −1.38683 | ||||||||
\(514\) | 26.0153 | 1.14748 | ||||||||
\(515\) | 4.34836 | 0.191612 | ||||||||
\(516\) | −7.42115 | −0.326698 | ||||||||
\(517\) | −7.22522 | −0.317765 | ||||||||
\(518\) | −10.1262 | −0.444918 | ||||||||
\(519\) | −42.3766 | −1.86013 | ||||||||
\(520\) | 0.751491 | 0.0329551 | ||||||||
\(521\) | 11.5950 | 0.507985 | 0.253993 | − | 0.967206i | \(-0.418256\pi\) | ||||
0.253993 | + | 0.967206i | \(0.418256\pi\) | |||||||
\(522\) | 3.72743 | 0.163145 | ||||||||
\(523\) | 36.8751 | 1.61244 | 0.806218 | − | 0.591619i | \(-0.201511\pi\) | ||||
0.806218 | + | 0.591619i | \(0.201511\pi\) | |||||||
\(524\) | 20.7507 | 0.906499 | ||||||||
\(525\) | 20.8166 | 0.908509 | ||||||||
\(526\) | −13.9916 | −0.610064 | ||||||||
\(527\) | −24.0133 | −1.04604 | ||||||||
\(528\) | −8.07713 | −0.351512 | ||||||||
\(529\) | 9.32628 | 0.405490 | ||||||||
\(530\) | 0.919462 | 0.0399389 | ||||||||
\(531\) | 1.77926 | 0.0772131 | ||||||||
\(532\) | −15.4526 | −0.669957 | ||||||||
\(533\) | 6.15349 | 0.266537 | ||||||||
\(534\) | −20.5750 | −0.890368 | ||||||||
\(535\) | 3.89915 | 0.168575 | ||||||||
\(536\) | −5.67176 | −0.244983 | ||||||||
\(537\) | −4.26413 | −0.184011 | ||||||||
\(538\) | 12.6808 | 0.546708 | ||||||||
\(539\) | −8.51897 | −0.366938 | ||||||||
\(540\) | 1.41633 | 0.0609490 | ||||||||
\(541\) | −42.6609 | −1.83414 | −0.917069 | − | 0.398729i | \(-0.869451\pi\) | ||||
−0.917069 | + | 0.398729i | \(0.869451\pi\) | |||||||
\(542\) | 0.812497 | 0.0348997 | ||||||||
\(543\) | −24.2046 | −1.03872 | ||||||||
\(544\) | 6.75619 | 0.289669 | ||||||||
\(545\) | −3.97667 | −0.170342 | ||||||||
\(546\) | −10.2363 | −0.438072 | ||||||||
\(547\) | 31.5506 | 1.34900 | 0.674502 | − | 0.738273i | \(-0.264358\pi\) | ||||
0.674502 | + | 0.738273i | \(0.264358\pi\) | |||||||
\(548\) | −9.23510 | −0.394504 | ||||||||
\(549\) | −4.39543 | −0.187592 | ||||||||
\(550\) | −20.8489 | −0.889002 | ||||||||
\(551\) | −42.3954 | −1.80610 | ||||||||
\(552\) | −10.7994 | −0.459652 | ||||||||
\(553\) | −4.64017 | −0.197320 | ||||||||
\(554\) | −2.28077 | −0.0969006 | ||||||||
\(555\) | 2.68206 | 0.113847 | ||||||||
\(556\) | −8.85808 | −0.375666 | ||||||||
\(557\) | 17.4739 | 0.740391 | 0.370195 | − | 0.928954i | \(-0.379291\pi\) | ||||
0.370195 | + | 0.928954i | \(0.379291\pi\) | |||||||
\(558\) | −2.16025 | −0.0914507 | ||||||||
\(559\) | 9.41957 | 0.398405 | ||||||||
\(560\) | 0.696762 | 0.0294436 | ||||||||
\(561\) | −54.5706 | −2.30397 | ||||||||
\(562\) | −21.2897 | −0.898051 | ||||||||
\(563\) | −18.4483 | −0.777503 | −0.388752 | − | 0.921343i | \(-0.627094\pi\) | ||||
−0.388752 | + | 0.921343i | \(0.627094\pi\) | |||||||
\(564\) | 3.22727 | 0.135893 | ||||||||
\(565\) | 2.40883 | 0.101340 | ||||||||
\(566\) | −23.5640 | −0.990469 | ||||||||
\(567\) | −23.3680 | −0.981364 | ||||||||
\(568\) | −11.3055 | −0.474368 | ||||||||
\(569\) | 22.1571 | 0.928874 | 0.464437 | − | 0.885606i | \(-0.346257\pi\) | ||||
0.464437 | + | 0.885606i | \(0.346257\pi\) | |||||||
\(570\) | 4.09286 | 0.171431 | ||||||||
\(571\) | −12.9261 | −0.540940 | −0.270470 | − | 0.962728i | \(-0.587179\pi\) | ||||
−0.270470 | + | 0.962728i | \(0.587179\pi\) | |||||||
\(572\) | 10.2522 | 0.428665 | ||||||||
\(573\) | −7.78753 | −0.325329 | ||||||||
\(574\) | 5.70535 | 0.238137 | ||||||||
\(575\) | −27.8757 | −1.16250 | ||||||||
\(576\) | 0.607790 | 0.0253246 | ||||||||
\(577\) | 14.4085 | 0.599832 | 0.299916 | − | 0.953966i | \(-0.403041\pi\) | ||||
0.299916 | + | 0.953966i | \(0.403041\pi\) | |||||||
\(578\) | 28.6461 | 1.19152 | ||||||||
\(579\) | −41.4459 | −1.72243 | ||||||||
\(580\) | 1.91161 | 0.0793753 | ||||||||
\(581\) | −4.39918 | −0.182509 | ||||||||
\(582\) | 15.7772 | 0.653985 | ||||||||
\(583\) | 12.5437 | 0.519508 | ||||||||
\(584\) | 13.3499 | 0.552423 | ||||||||
\(585\) | 0.456748 | 0.0188842 | ||||||||
\(586\) | 6.89229 | 0.284718 | ||||||||
\(587\) | −43.3978 | −1.79122 | −0.895609 | − | 0.444842i | \(-0.853260\pi\) | ||||
−0.895609 | + | 0.444842i | \(0.853260\pi\) | |||||||
\(588\) | 3.80515 | 0.156922 | ||||||||
\(589\) | 24.5704 | 1.01241 | ||||||||
\(590\) | 0.912491 | 0.0375667 | ||||||||
\(591\) | 16.5789 | 0.681967 | ||||||||
\(592\) | −4.53006 | −0.186184 | ||||||||
\(593\) | 16.3657 | 0.672061 | 0.336030 | − | 0.941851i | \(-0.390916\pi\) | ||||
0.336030 | + | 0.941851i | \(0.390916\pi\) | |||||||
\(594\) | 19.3222 | 0.792799 | ||||||||
\(595\) | 4.70745 | 0.192987 | ||||||||
\(596\) | 7.93318 | 0.324956 | ||||||||
\(597\) | 25.8278 | 1.05706 | ||||||||
\(598\) | 13.7075 | 0.560541 | ||||||||
\(599\) | −27.4661 | −1.12224 | −0.561118 | − | 0.827736i | \(-0.689629\pi\) | ||||
−0.561118 | + | 0.827736i | \(0.689629\pi\) | |||||||
\(600\) | 9.31254 | 0.380183 | ||||||||
\(601\) | −7.28260 | −0.297063 | −0.148532 | − | 0.988908i | \(-0.547455\pi\) | ||||
−0.148532 | + | 0.988908i | \(0.547455\pi\) | |||||||
\(602\) | 8.73356 | 0.355953 | ||||||||
\(603\) | −3.44724 | −0.140382 | ||||||||
\(604\) | −16.7113 | −0.679972 | ||||||||
\(605\) | 2.20783 | 0.0897611 | ||||||||
\(606\) | −4.36902 | −0.177479 | ||||||||
\(607\) | −23.0549 | −0.935768 | −0.467884 | − | 0.883790i | \(-0.654983\pi\) | ||||
−0.467884 | + | 0.883790i | \(0.654983\pi\) | |||||||
\(608\) | −6.91293 | −0.280356 | ||||||||
\(609\) | −26.0386 | −1.05514 | ||||||||
\(610\) | −2.25420 | −0.0912697 | ||||||||
\(611\) | −4.09633 | −0.165720 | ||||||||
\(612\) | 4.10634 | 0.165989 | ||||||||
\(613\) | 9.75106 | 0.393842 | 0.196921 | − | 0.980419i | \(-0.436906\pi\) | ||||
0.196921 | + | 0.980419i | \(0.436906\pi\) | |||||||
\(614\) | −18.3766 | −0.741619 | ||||||||
\(615\) | −1.51114 | −0.0609352 | ||||||||
\(616\) | 9.50554 | 0.382989 | ||||||||
\(617\) | 7.13955 | 0.287427 | 0.143714 | − | 0.989619i | \(-0.454096\pi\) | ||||
0.143714 | + | 0.989619i | \(0.454096\pi\) | |||||||
\(618\) | −26.4973 | −1.06588 | ||||||||
\(619\) | −39.9108 | −1.60415 | −0.802076 | − | 0.597222i | \(-0.796271\pi\) | ||||
−0.802076 | + | 0.597222i | \(0.796271\pi\) | |||||||
\(620\) | −1.10788 | −0.0444937 | ||||||||
\(621\) | 25.8344 | 1.03670 | ||||||||
\(622\) | −31.6409 | −1.26868 | ||||||||
\(623\) | 24.2136 | 0.970099 | ||||||||
\(624\) | −4.57932 | −0.183319 | ||||||||
\(625\) | 23.5520 | 0.942082 | ||||||||
\(626\) | −3.70011 | −0.147886 | ||||||||
\(627\) | 55.8366 | 2.22990 | ||||||||
\(628\) | 20.4744 | 0.817019 | ||||||||
\(629\) | −30.6059 | −1.22034 | ||||||||
\(630\) | 0.423485 | 0.0168720 | ||||||||
\(631\) | −26.4208 | −1.05179 | −0.525897 | − | 0.850548i | \(-0.676270\pi\) | ||||
−0.525897 | + | 0.850548i | \(0.676270\pi\) | |||||||
\(632\) | −2.07583 | −0.0825723 | ||||||||
\(633\) | 35.7490 | 1.42090 | ||||||||
\(634\) | −33.4390 | −1.32803 | ||||||||
\(635\) | −0.566586 | −0.0224843 | ||||||||
\(636\) | −5.60287 | −0.222168 | ||||||||
\(637\) | −4.82982 | −0.191365 | ||||||||
\(638\) | 26.0791 | 1.03248 | ||||||||
\(639\) | −6.87137 | −0.271827 | ||||||||
\(640\) | 0.311705 | 0.0123212 | ||||||||
\(641\) | −21.0392 | −0.830997 | −0.415499 | − | 0.909594i | \(-0.636393\pi\) | ||||
−0.415499 | + | 0.909594i | \(0.636393\pi\) | |||||||
\(642\) | −23.7600 | −0.937734 | ||||||||
\(643\) | −26.7612 | −1.05536 | −0.527679 | − | 0.849444i | \(-0.676938\pi\) | ||||
−0.527679 | + | 0.849444i | \(0.676938\pi\) | |||||||
\(644\) | 12.7092 | 0.500813 | ||||||||
\(645\) | −2.31321 | −0.0910825 | ||||||||
\(646\) | −46.7051 | −1.83759 | ||||||||
\(647\) | −39.7126 | −1.56126 | −0.780632 | − | 0.624991i | \(-0.785103\pi\) | ||||
−0.780632 | + | 0.624991i | \(0.785103\pi\) | |||||||
\(648\) | −10.4540 | −0.410670 | ||||||||
\(649\) | 12.4486 | 0.488651 | ||||||||
\(650\) | −11.8203 | −0.463630 | ||||||||
\(651\) | 15.0908 | 0.591455 | ||||||||
\(652\) | 9.00051 | 0.352487 | ||||||||
\(653\) | 22.9967 | 0.899929 | 0.449965 | − | 0.893046i | \(-0.351437\pi\) | ||||
0.449965 | + | 0.893046i | \(0.351437\pi\) | |||||||
\(654\) | 24.2324 | 0.947563 | ||||||||
\(655\) | 6.46809 | 0.252729 | ||||||||
\(656\) | 2.55236 | 0.0996528 | ||||||||
\(657\) | 8.11393 | 0.316555 | ||||||||
\(658\) | −3.79800 | −0.148062 | ||||||||
\(659\) | −2.43847 | −0.0949893 | −0.0474947 | − | 0.998871i | \(-0.515124\pi\) | ||||
−0.0474947 | + | 0.998871i | \(0.515124\pi\) | |||||||
\(660\) | −2.51768 | −0.0980005 | ||||||||
\(661\) | 13.3573 | 0.519539 | 0.259770 | − | 0.965671i | \(-0.416353\pi\) | ||||
0.259770 | + | 0.965671i | \(0.416353\pi\) | |||||||
\(662\) | 25.9855 | 1.00996 | ||||||||
\(663\) | −30.9387 | −1.20156 | ||||||||
\(664\) | −1.96803 | −0.0763743 | ||||||||
\(665\) | −4.81667 | −0.186782 | ||||||||
\(666\) | −2.75332 | −0.106689 | ||||||||
\(667\) | 34.8686 | 1.35012 | ||||||||
\(668\) | −8.99976 | −0.348211 | ||||||||
\(669\) | −24.7150 | −0.955535 | ||||||||
\(670\) | −1.76791 | −0.0683005 | ||||||||
\(671\) | −30.7528 | −1.18720 | ||||||||
\(672\) | −4.24582 | −0.163786 | ||||||||
\(673\) | −12.5602 | −0.484159 | −0.242079 | − | 0.970256i | \(-0.577829\pi\) | ||||
−0.242079 | + | 0.970256i | \(0.577829\pi\) | |||||||
\(674\) | 25.7759 | 0.992850 | ||||||||
\(675\) | −22.2776 | −0.857464 | ||||||||
\(676\) | −7.18754 | −0.276444 | ||||||||
\(677\) | 27.5481 | 1.05876 | 0.529380 | − | 0.848385i | \(-0.322424\pi\) | ||||
0.529380 | + | 0.848385i | \(0.322424\pi\) | |||||||
\(678\) | −14.6785 | −0.563725 | ||||||||
\(679\) | −18.5673 | −0.712549 | ||||||||
\(680\) | 2.10594 | 0.0807590 | ||||||||
\(681\) | −48.5263 | −1.85953 | ||||||||
\(682\) | −15.1143 | −0.578755 | ||||||||
\(683\) | 14.1796 | 0.542566 | 0.271283 | − | 0.962500i | \(-0.412552\pi\) | ||||
0.271283 | + | 0.962500i | \(0.412552\pi\) | |||||||
\(684\) | −4.20161 | −0.160653 | ||||||||
\(685\) | −2.87863 | −0.109987 | ||||||||
\(686\) | −20.1254 | −0.768389 | ||||||||
\(687\) | −19.3564 | −0.738493 | ||||||||
\(688\) | 3.90707 | 0.148956 | ||||||||
\(689\) | 7.11165 | 0.270932 | ||||||||
\(690\) | −3.36622 | −0.128150 | ||||||||
\(691\) | 32.3025 | 1.22885 | 0.614423 | − | 0.788977i | \(-0.289389\pi\) | ||||
0.614423 | + | 0.788977i | \(0.289389\pi\) | |||||||
\(692\) | 22.3103 | 0.848111 | ||||||||
\(693\) | 5.77737 | 0.219464 | ||||||||
\(694\) | −4.89860 | −0.185948 | ||||||||
\(695\) | −2.76111 | −0.104735 | ||||||||
\(696\) | −11.6487 | −0.441542 | ||||||||
\(697\) | 17.2442 | 0.653171 | ||||||||
\(698\) | 9.62083 | 0.364154 | ||||||||
\(699\) | 48.1676 | 1.82187 | ||||||||
\(700\) | −10.9594 | −0.414228 | ||||||||
\(701\) | 44.5686 | 1.68333 | 0.841667 | − | 0.539997i | \(-0.181575\pi\) | ||||
0.841667 | + | 0.539997i | \(0.181575\pi\) | |||||||
\(702\) | 10.9547 | 0.413458 | ||||||||
\(703\) | 31.3160 | 1.18110 | ||||||||
\(704\) | 4.25242 | 0.160269 | ||||||||
\(705\) | 1.00596 | 0.0378865 | ||||||||
\(706\) | 6.69700 | 0.252045 | ||||||||
\(707\) | 5.14167 | 0.193372 | ||||||||
\(708\) | −5.56039 | −0.208972 | ||||||||
\(709\) | −19.6662 | −0.738580 | −0.369290 | − | 0.929314i | \(-0.620399\pi\) | ||||
−0.369290 | + | 0.929314i | \(0.620399\pi\) | |||||||
\(710\) | −3.52398 | −0.132253 | ||||||||
\(711\) | −1.26167 | −0.0473164 | ||||||||
\(712\) | 10.8323 | 0.405957 | ||||||||
\(713\) | −20.2082 | −0.756805 | ||||||||
\(714\) | −28.6855 | −1.07353 | ||||||||
\(715\) | 3.19566 | 0.119511 | ||||||||
\(716\) | 2.24497 | 0.0838983 | ||||||||
\(717\) | −36.0652 | −1.34688 | ||||||||
\(718\) | 22.8379 | 0.852303 | ||||||||
\(719\) | 31.3422 | 1.16887 | 0.584433 | − | 0.811442i | \(-0.301317\pi\) | ||||
0.584433 | + | 0.811442i | \(0.301317\pi\) | |||||||
\(720\) | 0.189451 | 0.00706042 | ||||||||
\(721\) | 31.1833 | 1.16133 | ||||||||
\(722\) | 28.7886 | 1.07140 | ||||||||
\(723\) | −37.3971 | −1.39081 | ||||||||
\(724\) | 12.7432 | 0.473597 | ||||||||
\(725\) | −30.0679 | −1.11670 | ||||||||
\(726\) | −13.4537 | −0.499315 | ||||||||
\(727\) | 17.0344 | 0.631772 | 0.315886 | − | 0.948797i | \(-0.397698\pi\) | ||||
0.315886 | + | 0.948797i | \(0.397698\pi\) | |||||||
\(728\) | 5.38916 | 0.199735 | ||||||||
\(729\) | 19.5380 | 0.723628 | ||||||||
\(730\) | 4.16123 | 0.154014 | ||||||||
\(731\) | 26.3969 | 0.976324 | ||||||||
\(732\) | 13.7363 | 0.507707 | ||||||||
\(733\) | 29.7272 | 1.09800 | 0.548999 | − | 0.835823i | \(-0.315009\pi\) | ||||
0.548999 | + | 0.835823i | \(0.315009\pi\) | |||||||
\(734\) | −3.88121 | −0.143258 | ||||||||
\(735\) | 1.18608 | 0.0437493 | ||||||||
\(736\) | 5.68562 | 0.209575 | ||||||||
\(737\) | −24.1187 | −0.888424 | ||||||||
\(738\) | 1.55130 | 0.0571040 | ||||||||
\(739\) | −25.5193 | −0.938743 | −0.469371 | − | 0.883001i | \(-0.655519\pi\) | ||||
−0.469371 | + | 0.883001i | \(0.655519\pi\) | |||||||
\(740\) | −1.41204 | −0.0519077 | ||||||||
\(741\) | 31.6565 | 1.16293 | ||||||||
\(742\) | 6.59373 | 0.242063 | ||||||||
\(743\) | −10.6610 | −0.391115 | −0.195557 | − | 0.980692i | \(-0.562652\pi\) | ||||
−0.195557 | + | 0.980692i | \(0.562652\pi\) | |||||||
\(744\) | 6.75105 | 0.247505 | ||||||||
\(745\) | 2.47281 | 0.0905968 | ||||||||
\(746\) | 29.4760 | 1.07919 | ||||||||
\(747\) | −1.19615 | −0.0437647 | ||||||||
\(748\) | 28.7302 | 1.05048 | ||||||||
\(749\) | 27.9619 | 1.02171 | ||||||||
\(750\) | 5.86305 | 0.214088 | ||||||||
\(751\) | 34.4688 | 1.25779 | 0.628893 | − | 0.777492i | \(-0.283509\pi\) | ||||
0.628893 | + | 0.777492i | \(0.283509\pi\) | |||||||
\(752\) | −1.69908 | −0.0619592 | ||||||||
\(753\) | 0.809772 | 0.0295097 | ||||||||
\(754\) | 14.7855 | 0.538456 | ||||||||
\(755\) | −5.20898 | −0.189574 | ||||||||
\(756\) | 10.1569 | 0.369402 | ||||||||
\(757\) | −51.2999 | −1.86453 | −0.932263 | − | 0.361781i | \(-0.882169\pi\) | ||||
−0.932263 | + | 0.361781i | \(0.882169\pi\) | |||||||
\(758\) | −34.7667 | −1.26278 | ||||||||
\(759\) | −45.9235 | −1.66692 | ||||||||
\(760\) | −2.15479 | −0.0781626 | ||||||||
\(761\) | 6.00389 | 0.217641 | 0.108820 | − | 0.994061i | \(-0.465293\pi\) | ||||
0.108820 | + | 0.994061i | \(0.465293\pi\) | |||||||
\(762\) | 3.45257 | 0.125073 | ||||||||
\(763\) | −28.5179 | −1.03242 | ||||||||
\(764\) | 4.09996 | 0.148331 | ||||||||
\(765\) | 1.27997 | 0.0462773 | ||||||||
\(766\) | −24.4903 | −0.884870 | ||||||||
\(767\) | 7.05773 | 0.254840 | ||||||||
\(768\) | −1.89942 | −0.0685394 | ||||||||
\(769\) | −26.9147 | −0.970571 | −0.485285 | − | 0.874356i | \(-0.661284\pi\) | ||||
−0.485285 | + | 0.874356i | \(0.661284\pi\) | |||||||
\(770\) | 2.96292 | 0.106776 | ||||||||
\(771\) | −49.4139 | −1.77960 | ||||||||
\(772\) | 21.8203 | 0.785331 | ||||||||
\(773\) | −33.1476 | −1.19223 | −0.596117 | − | 0.802897i | \(-0.703291\pi\) | ||||
−0.596117 | + | 0.802897i | \(0.703291\pi\) | |||||||
\(774\) | 2.37468 | 0.0853559 | ||||||||
\(775\) | 17.4260 | 0.625961 | ||||||||
\(776\) | −8.30633 | −0.298180 | ||||||||
\(777\) | 19.2338 | 0.690009 | ||||||||
\(778\) | −13.4112 | −0.480815 | ||||||||
\(779\) | −17.6443 | −0.632172 | ||||||||
\(780\) | −1.42740 | −0.0511090 | ||||||||
\(781\) | −48.0757 | −1.72029 | ||||||||
\(782\) | 38.4131 | 1.37365 | ||||||||
\(783\) | 27.8661 | 0.995853 | ||||||||
\(784\) | −2.00332 | −0.0715472 | ||||||||
\(785\) | 6.38198 | 0.227783 | ||||||||
\(786\) | −39.4143 | −1.40586 | ||||||||
\(787\) | −13.2726 | −0.473116 | −0.236558 | − | 0.971617i | \(-0.576019\pi\) | ||||
−0.236558 | + | 0.971617i | \(0.576019\pi\) | |||||||
\(788\) | −8.72843 | −0.310938 | ||||||||
\(789\) | 26.5760 | 0.946129 | ||||||||
\(790\) | −0.647048 | −0.0230209 | ||||||||
\(791\) | 17.2744 | 0.614206 | ||||||||
\(792\) | 2.58458 | 0.0918390 | ||||||||
\(793\) | −17.4353 | −0.619144 | ||||||||
\(794\) | 10.1924 | 0.361715 | ||||||||
\(795\) | −1.74644 | −0.0619399 | ||||||||
\(796\) | −13.5977 | −0.481959 | ||||||||
\(797\) | 9.92091 | 0.351417 | 0.175708 | − | 0.984442i | \(-0.443778\pi\) | ||||
0.175708 | + | 0.984442i | \(0.443778\pi\) | |||||||
\(798\) | 29.3510 | 1.03902 | ||||||||
\(799\) | −11.4793 | −0.406109 | ||||||||
\(800\) | −4.90284 | −0.173342 | ||||||||
\(801\) | 6.58374 | 0.232625 | ||||||||
\(802\) | −13.8909 | −0.490504 | ||||||||
\(803\) | 56.7694 | 2.00335 | ||||||||
\(804\) | 10.7730 | 0.379936 | ||||||||
\(805\) | 3.96152 | 0.139625 | ||||||||
\(806\) | −8.56901 | −0.301831 | ||||||||
\(807\) | −24.0862 | −0.847873 | ||||||||
\(808\) | 2.30019 | 0.0809203 | ||||||||
\(809\) | −39.7460 | −1.39740 | −0.698698 | − | 0.715417i | \(-0.746237\pi\) | ||||
−0.698698 | + | 0.715417i | \(0.746237\pi\) | |||||||
\(810\) | −3.25855 | −0.114494 | ||||||||
\(811\) | −0.443439 | −0.0155713 | −0.00778563 | − | 0.999970i | \(-0.502478\pi\) | ||||
−0.00778563 | + | 0.999970i | \(0.502478\pi\) | |||||||
\(812\) | 13.7087 | 0.481082 | ||||||||
\(813\) | −1.54327 | −0.0541249 | ||||||||
\(814\) | −19.2637 | −0.675193 | ||||||||
\(815\) | 2.80550 | 0.0982724 | ||||||||
\(816\) | −12.8328 | −0.449239 | ||||||||
\(817\) | −27.0093 | −0.944935 | ||||||||
\(818\) | −10.4113 | −0.364023 | ||||||||
\(819\) | 3.27547 | 0.114454 | ||||||||
\(820\) | 0.795582 | 0.0277829 | ||||||||
\(821\) | 27.8231 | 0.971034 | 0.485517 | − | 0.874227i | \(-0.338631\pi\) | ||||
0.485517 | + | 0.874227i | \(0.338631\pi\) | |||||||
\(822\) | 17.5413 | 0.611824 | ||||||||
\(823\) | −26.9019 | −0.937741 | −0.468871 | − | 0.883267i | \(-0.655339\pi\) | ||||
−0.468871 | + | 0.883267i | \(0.655339\pi\) | |||||||
\(824\) | 13.9502 | 0.485980 | ||||||||
\(825\) | 39.6009 | 1.37872 | ||||||||
\(826\) | 6.54373 | 0.227686 | ||||||||
\(827\) | 12.6344 | 0.439339 | 0.219670 | − | 0.975574i | \(-0.429502\pi\) | ||||
0.219670 | + | 0.975574i | \(0.429502\pi\) | |||||||
\(828\) | 3.45566 | 0.120093 | ||||||||
\(829\) | −13.9741 | −0.485340 | −0.242670 | − | 0.970109i | \(-0.578023\pi\) | ||||
−0.242670 | + | 0.970109i | \(0.578023\pi\) | |||||||
\(830\) | −0.613444 | −0.0212929 | ||||||||
\(831\) | 4.33213 | 0.150280 | ||||||||
\(832\) | 2.41091 | 0.0835831 | ||||||||
\(833\) | −13.5348 | −0.468954 | ||||||||
\(834\) | 16.8252 | 0.582609 | ||||||||
\(835\) | −2.80527 | −0.0970804 | ||||||||
\(836\) | −29.3967 | −1.01671 | ||||||||
\(837\) | −16.1499 | −0.558223 | ||||||||
\(838\) | −31.1890 | −1.07741 | ||||||||
\(839\) | −23.5561 | −0.813248 | −0.406624 | − | 0.913596i | \(-0.633294\pi\) | ||||
−0.406624 | + | 0.913596i | \(0.633294\pi\) | |||||||
\(840\) | −1.32344 | −0.0456631 | ||||||||
\(841\) | 8.61076 | 0.296923 | ||||||||
\(842\) | −13.4321 | −0.462899 | ||||||||
\(843\) | 40.4380 | 1.39276 | ||||||||
\(844\) | −18.8210 | −0.647847 | ||||||||
\(845\) | −2.24039 | −0.0770717 | ||||||||
\(846\) | −1.03269 | −0.0355044 | ||||||||
\(847\) | 15.8330 | 0.544028 | ||||||||
\(848\) | 2.94978 | 0.101296 | ||||||||
\(849\) | 44.7579 | 1.53609 | ||||||||
\(850\) | −33.1245 | −1.13616 | ||||||||
\(851\) | −25.7562 | −0.882911 | ||||||||
\(852\) | 21.4739 | 0.735683 | ||||||||
\(853\) | 8.49265 | 0.290783 | 0.145391 | − | 0.989374i | \(-0.453556\pi\) | ||||
0.145391 | + | 0.989374i | \(0.453556\pi\) | |||||||
\(854\) | −16.1655 | −0.553172 | ||||||||
\(855\) | −1.30966 | −0.0447895 | ||||||||
\(856\) | 12.5091 | 0.427553 | ||||||||
\(857\) | −3.80023 | −0.129813 | −0.0649067 | − | 0.997891i | \(-0.520675\pi\) | ||||
−0.0649067 | + | 0.997891i | \(0.520675\pi\) | |||||||
\(858\) | −19.4732 | −0.664804 | ||||||||
\(859\) | −26.0746 | −0.889655 | −0.444827 | − | 0.895616i | \(-0.646735\pi\) | ||||
−0.444827 | + | 0.895616i | \(0.646735\pi\) | |||||||
\(860\) | 1.21785 | 0.0415284 | ||||||||
\(861\) | −10.8368 | −0.369319 | ||||||||
\(862\) | 25.7669 | 0.877623 | ||||||||
\(863\) | −0.305476 | −0.0103985 | −0.00519925 | − | 0.999986i | \(-0.501655\pi\) | ||||
−0.00519925 | + | 0.999986i | \(0.501655\pi\) | |||||||
\(864\) | 4.54381 | 0.154583 | ||||||||
\(865\) | 6.95424 | 0.236451 | ||||||||
\(866\) | −31.6498 | −1.07550 | ||||||||
\(867\) | −54.4109 | −1.84789 | ||||||||
\(868\) | −7.94495 | −0.269669 | ||||||||
\(869\) | −8.82732 | −0.299446 | ||||||||
\(870\) | −3.63095 | −0.123101 | ||||||||
\(871\) | −13.6741 | −0.463328 | ||||||||
\(872\) | −12.7578 | −0.432034 | ||||||||
\(873\) | −5.04850 | −0.170866 | ||||||||
\(874\) | −39.3043 | −1.32949 | ||||||||
\(875\) | −6.89992 | −0.233260 | ||||||||
\(876\) | −25.3570 | −0.856735 | ||||||||
\(877\) | −42.4868 | −1.43468 | −0.717339 | − | 0.696725i | \(-0.754640\pi\) | ||||
−0.717339 | + | 0.696725i | \(0.754640\pi\) | |||||||
\(878\) | −22.3643 | −0.754758 | ||||||||
\(879\) | −13.0913 | −0.441560 | ||||||||
\(880\) | 1.32550 | 0.0446826 | ||||||||
\(881\) | −40.5786 | −1.36713 | −0.683564 | − | 0.729891i | \(-0.739571\pi\) | ||||
−0.683564 | + | 0.729891i | \(0.739571\pi\) | |||||||
\(882\) | −1.21760 | −0.0409987 | ||||||||
\(883\) | 6.01375 | 0.202379 | 0.101189 | − | 0.994867i | \(-0.467735\pi\) | ||||
0.101189 | + | 0.994867i | \(0.467735\pi\) | |||||||
\(884\) | 16.2885 | 0.547843 | ||||||||
\(885\) | −1.73320 | −0.0582609 | ||||||||
\(886\) | 30.5556 | 1.02654 | ||||||||
\(887\) | −12.5847 | −0.422554 | −0.211277 | − | 0.977426i | \(-0.567762\pi\) | ||||
−0.211277 | + | 0.977426i | \(0.567762\pi\) | |||||||
\(888\) | 8.60448 | 0.288747 | ||||||||
\(889\) | −4.06315 | −0.136274 | ||||||||
\(890\) | 3.37647 | 0.113180 | ||||||||
\(891\) | −44.4546 | −1.48929 | ||||||||
\(892\) | 13.0119 | 0.435669 | ||||||||
\(893\) | 11.7456 | 0.393053 | ||||||||
\(894\) | −15.0684 | −0.503964 | ||||||||
\(895\) | 0.699767 | 0.0233906 | ||||||||
\(896\) | 2.23532 | 0.0746770 | ||||||||
\(897\) | −26.0363 | −0.869325 | ||||||||
\(898\) | 24.7092 | 0.824556 | ||||||||
\(899\) | −21.7975 | −0.726987 | ||||||||
\(900\) | −2.97990 | −0.0993299 | ||||||||
\(901\) | 19.9293 | 0.663941 | ||||||||
\(902\) | 10.8537 | 0.361389 | ||||||||
\(903\) | −16.5887 | −0.552037 | ||||||||
\(904\) | 7.72790 | 0.257026 | ||||||||
\(905\) | 3.97211 | 0.132038 | ||||||||
\(906\) | 31.7417 | 1.05455 | ||||||||
\(907\) | −51.6994 | −1.71665 | −0.858325 | − | 0.513106i | \(-0.828495\pi\) | ||||
−0.858325 | + | 0.513106i | \(0.828495\pi\) | |||||||
\(908\) | 25.5480 | 0.847840 | ||||||||
\(909\) | 1.39803 | 0.0463697 | ||||||||
\(910\) | 1.67983 | 0.0556857 | ||||||||
\(911\) | −50.3053 | −1.66669 | −0.833344 | − | 0.552754i | \(-0.813577\pi\) | ||||
−0.833344 | + | 0.552754i | \(0.813577\pi\) | |||||||
\(912\) | 13.1305 | 0.434796 | ||||||||
\(913\) | −8.36888 | −0.276970 | ||||||||
\(914\) | −37.6152 | −1.24420 | ||||||||
\(915\) | 4.28166 | 0.141547 | ||||||||
\(916\) | 10.1907 | 0.336710 | ||||||||
\(917\) | 46.3846 | 1.53175 | ||||||||
\(918\) | 30.6988 | 1.01321 | ||||||||
\(919\) | −52.6615 | −1.73714 | −0.868572 | − | 0.495563i | \(-0.834962\pi\) | ||||
−0.868572 | + | 0.495563i | \(0.834962\pi\) | |||||||
\(920\) | 1.77224 | 0.0584289 | ||||||||
\(921\) | 34.9048 | 1.15015 | ||||||||
\(922\) | 12.8721 | 0.423922 | ||||||||
\(923\) | −27.2565 | −0.897158 | ||||||||
\(924\) | −18.0550 | −0.593966 | ||||||||
\(925\) | 22.2102 | 0.730265 | ||||||||
\(926\) | 32.6181 | 1.07190 | ||||||||
\(927\) | 8.47881 | 0.278481 | ||||||||
\(928\) | 6.13276 | 0.201318 | ||||||||
\(929\) | 41.1839 | 1.35120 | 0.675599 | − | 0.737269i | \(-0.263885\pi\) | ||||
0.675599 | + | 0.737269i | \(0.263885\pi\) | |||||||
\(930\) | 2.10433 | 0.0690039 | ||||||||
\(931\) | 13.8488 | 0.453877 | ||||||||
\(932\) | −25.3591 | −0.830666 | ||||||||
\(933\) | 60.0993 | 1.96756 | ||||||||
\(934\) | −4.90131 | −0.160376 | ||||||||
\(935\) | 8.95533 | 0.292871 | ||||||||
\(936\) | 1.46532 | 0.0478956 | ||||||||
\(937\) | 19.1598 | 0.625922 | 0.312961 | − | 0.949766i | \(-0.398679\pi\) | ||||
0.312961 | + | 0.949766i | \(0.398679\pi\) | |||||||
\(938\) | −12.6782 | −0.413959 | ||||||||
\(939\) | 7.02805 | 0.229352 | ||||||||
\(940\) | −0.529612 | −0.0172741 | ||||||||
\(941\) | 9.23612 | 0.301089 | 0.150544 | − | 0.988603i | \(-0.451897\pi\) | ||||
0.150544 | + | 0.988603i | \(0.451897\pi\) | |||||||
\(942\) | −38.8895 | −1.26709 | ||||||||
\(943\) | 14.5117 | 0.472567 | ||||||||
\(944\) | 2.92742 | 0.0952794 | ||||||||
\(945\) | 3.16595 | 0.102988 | ||||||||
\(946\) | 16.6145 | 0.540184 | ||||||||
\(947\) | −44.5273 | −1.44694 | −0.723472 | − | 0.690354i | \(-0.757455\pi\) | ||||
−0.723472 | + | 0.690354i | \(0.757455\pi\) | |||||||
\(948\) | 3.94288 | 0.128059 | ||||||||
\(949\) | 32.1853 | 1.04478 | ||||||||
\(950\) | 33.8930 | 1.09963 | ||||||||
\(951\) | 63.5147 | 2.05961 | ||||||||
\(952\) | 15.1023 | 0.489468 | ||||||||
\(953\) | 33.5663 | 1.08732 | 0.543659 | − | 0.839306i | \(-0.317038\pi\) | ||||
0.543659 | + | 0.839306i | \(0.317038\pi\) | |||||||
\(954\) | 1.79285 | 0.0580456 | ||||||||
\(955\) | 1.27798 | 0.0413543 | ||||||||
\(956\) | 18.9875 | 0.614099 | ||||||||
\(957\) | −49.5351 | −1.60124 | ||||||||
\(958\) | −3.59924 | −0.116286 | ||||||||
\(959\) | −20.6435 | −0.666612 | ||||||||
\(960\) | −0.592058 | −0.0191086 | ||||||||
\(961\) | −18.3671 | −0.592489 | ||||||||
\(962\) | −10.9215 | −0.352125 | ||||||||
\(963\) | 7.60291 | 0.245000 | ||||||||
\(964\) | 19.6887 | 0.634130 | ||||||||
\(965\) | 6.80150 | 0.218948 | ||||||||
\(966\) | −24.1401 | −0.776695 | ||||||||
\(967\) | −57.7362 | −1.85667 | −0.928336 | − | 0.371742i | \(-0.878760\pi\) | ||||
−0.928336 | + | 0.371742i | \(0.878760\pi\) | |||||||
\(968\) | 7.08308 | 0.227659 | ||||||||
\(969\) | 88.7125 | 2.84985 | ||||||||
\(970\) | −2.58912 | −0.0831317 | ||||||||
\(971\) | 2.55938 | 0.0821343 | 0.0410671 | − | 0.999156i | \(-0.486924\pi\) | ||||
0.0410671 | + | 0.999156i | \(0.486924\pi\) | |||||||
\(972\) | 6.22502 | 0.199668 | ||||||||
\(973\) | −19.8007 | −0.634781 | ||||||||
\(974\) | 0.985032 | 0.0315625 | ||||||||
\(975\) | 22.4517 | 0.719029 | ||||||||
\(976\) | −7.23183 | −0.231485 | ||||||||
\(977\) | −21.4124 | −0.685045 | −0.342522 | − | 0.939510i | \(-0.611281\pi\) | ||||
−0.342522 | + | 0.939510i | \(0.611281\pi\) | |||||||
\(978\) | −17.0957 | −0.546661 | ||||||||
\(979\) | 46.0634 | 1.47219 | ||||||||
\(980\) | −0.624445 | −0.0199472 | ||||||||
\(981\) | −7.75407 | −0.247568 | ||||||||
\(982\) | −29.3140 | −0.935447 | ||||||||
\(983\) | −55.2441 | −1.76201 | −0.881006 | − | 0.473104i | \(-0.843133\pi\) | ||||
−0.881006 | + | 0.473104i | \(0.843133\pi\) | |||||||
\(984\) | −4.84799 | −0.154548 | ||||||||
\(985\) | −2.72069 | −0.0866885 | ||||||||
\(986\) | 41.4341 | 1.31953 | ||||||||
\(987\) | 7.21399 | 0.229624 | ||||||||
\(988\) | −16.6664 | −0.530230 | ||||||||
\(989\) | 22.2141 | 0.706367 | ||||||||
\(990\) | 0.805625 | 0.0256045 | ||||||||
\(991\) | −24.2286 | −0.769646 | −0.384823 | − | 0.922990i | \(-0.625738\pi\) | ||||
−0.384823 | + | 0.922990i | \(0.625738\pi\) | |||||||
\(992\) | −3.55427 | −0.112848 | ||||||||
\(993\) | −49.3574 | −1.56631 | ||||||||
\(994\) | −25.2715 | −0.801562 | ||||||||
\(995\) | −4.23848 | −0.134369 | ||||||||
\(996\) | 3.73811 | 0.118446 | ||||||||
\(997\) | −1.27296 | −0.0403149 | −0.0201575 | − | 0.999797i | \(-0.506417\pi\) | ||||
−0.0201575 | + | 0.999797i | \(0.506417\pi\) | |||||||
\(998\) | −6.20797 | −0.196510 | ||||||||
\(999\) | −20.5837 | −0.651240 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4034.2.a.d.1.10 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.d.1.10 | ✓ | 52 | 1.1 | even | 1 | trivial |